Answer:
(a) ω = 1.57 rad/s
(b) ac = 4.92 m/s²
(c) μs = 0.5
Explanation:
(a)
The angular speed of the merry go-round can be found as follows:
ω = 2πf
where,
ω = angular speed = ?
f = frequency = 0.25 rev/s
Therefore,
ω = (2π)(0.25 rev/s)
<u>ω = 1.57 rad/s
</u>
(b)
The centripetal acceleration can be found as:
ac = v²/R
but,
v = Rω
Therefore,
ac = (Rω)²/R
ac = Rω²
therefore,
ac = (2 m)(1.57 rad/s)²
<u>ac = 4.92 m/s²
</u>
(c)
In order to avoid slipping the centripetal force must not exceed the frictional force between shoes and floor:
Centripetal Force = Frictional Force
m*ac = μs*R = μs*W
m*ac = μs*mg
ac = μs*g
μs = ac/g
μs = (4.92 m/s²)/(9.8 m/s²)
<u>μs = 0.5</u>
Answer: D(t)= 50(4/5)^t
Explanation: If 1/5 of the temperature difference is lost each minute, that means 4/5 of the difference remains each minute. So each minute, the temperature difference is multiplied by a factor of 4/5 (or 0.8).
If we start with the initial temperature difference, 50° Celsius, and keep multiplying by 4/5, this function gives us the temperature difference t minutes after the cake was put in the cooler.
Answer:
= 925.92 N
≅ 926N
Explanation:
Pressure due to car = pressure due to applied force
12000/18^2 = Force / 5^2
force = 12000 * 25/ 324
= 925.92 N
For equilibrium
Pressure1 = Pressure2
A1F1 = A2F2
12000*pi*(5^2) = F2 ( pi)*(18^2)
so, F2 = Applied force to lift car = 925.92 N
Pascal's principle
Pressure1 = Pressure2
F1/A1 = F2/A2 (F=force and A=area)
A1 =Pi*(0.05)²
A2 =Pi(0.18)²
F2=12000
F1 = 12000*(0.05)² / (0.18)² = 926N
Answer:
the power that can be generated by the river is 117.6 MW
Explanation:
Given that;
Volume flow rate of river v = 240 m³/s
Height above the lake surface a h = 50 m
Amount of power can be generated from this river water after the dam is filled = ?
Now the collected water in the dam contains potential energy which is used for the power generation,
hence, total mechanical energy is due to potential energy alone.
= m(gh)
first we determine the mass flow rate of the fluid m
m = p×v
where p is density ( 1000 kg/m³
so we substitute
m = 1000kg/m³ × 240 m³/s
m = 240000 kg/s
so we plug in our values into ( = m(gh) kJ/kg )
= 240000 × 9.8 × 50
= 117600000 W
= 117.6 MW
Therefore, the power that can be generated by the river is 117.6 MW
Answer:
True
Explanation:
This can be explained by the special theory of relativity for length contraction.
Length contraction is observed in the direction of motion of an object when an object moves with speed closer to the speed of light.
The length of the rocket in this case, appears shorter to the observer on earth in the stationary reference frame which is improper frame whereas the traveler in the rocket is in the same inertial frame which is proper for the rocket's size measurement.
